The 33,000 U.S. troops ordered to Afghanistan two years ago to stop Taliban advances are back home, with military officials claiming that the surge accomplished its objectives.

But did it?

“In mid-2009 there was a real risk that the mission in Afghanistan might very well fail,” Defense Secretary Leon Panetta said recently. “Today the situation is very much different and improved.”

Violence is down, Panetta said, echoing a refrain heard around the Pentagon.

But for all the American blood and treasure invested in the war, some experts who’ve studied it contend that the problem with the military’s claims of success is that the numbers don’t add up. Using them alone, the Taliban is overmatched, and attacks since the surge are down. Yet, they have become more brazen.

“When I was in the Pentagon, I used to see reams of metrics for Iraq and Afghanistan,” said Thomas Mahnken, a former deputy assistant defense secretary for policy planning under Presidents Barack Obama and George W. Bush. “Few had any real meaning.”

Now in its second decade, the war played a supporting role for many years while most of the military and political attention was focused on Iraq. And while the presidential campaign has occasionally veered to foreign policy concerns, like Libya and Syria, Afghanistan as an issue has been missing in action.

Obama and Republican challenger Mitt Romney largely agree on the strategy, which is to remove most American troops by the end 2014.

But after 11 years, Afghanistan remains a battlefield of mixed accomplishments and unforeseen milestones.

Last month marked the death of the 2,000th American service member in the war. It also saw a group of uniformed Afghan soldiers – our supposed allies – turned their weapons on American troops at an Afghan Army checkpoint. It was not the first time. So-called “green-on-blue” attacks have been increasing over the past year.

The end of the surge leaves the American military and NATO with a combined force of about 100,000, supplemented by an Afghan force of 350,000, according to NATO.

NATO and the Pentagon estimate that the Taliban has about 20,000 men. By any definition, the 20-to-1 odds would seem to pose an overwhelming advantage.

But a recent spate of highly organized attacks against allied forces, such as the raid last month in which 15 Taliban got inside Camp Bastion , a major air base in southern Afghanistan’s Helmand province, and killed two U.S. Marines and destroyed six fighter jets, indicate that troop numbers don’t tell the whole story.

Nor do the enemy body counts.

Coming up with numbers to reflect military progress has never been easy, said Mahnken, who teaches national security at the U.S. Naval War College. Even as basic a measure as the number of enemy killed has little meaning against an insurgency, he said.

In fact, military officials refuse to even track exact numbers of enemy killed or captured in Afghanistan. Instead, daily reports from the International Security Assistance Force, the NATO-led coalition, use vague descriptions like “few” or “several,” “multiple” or “numerous;” even “many.”

The measurements can mean anywhere from three to “more than 20.”

Using that math, U.S. and allied forces during the first half of September captured or killed about 400 insurgents. But if the entire Taliban force consists of about 20,000 fighters, shouldn’t losing hundreds every few weeks be a sign of a looming collapse?

Indeed, Mahnken said that by U.S. and NATO counts, the Taliban has been defeated several times over.

While Defense Department officials were shocked at the Camp Bastion incident, they say that insurgent attacks are down 24 percent since their peak in 2010, at the beginning of the surge, according to international security force numbers.

In 2010, between the May and August fighting season in Afghanistan, there were about 14,000 insurgent attacks, according the group’s statistics, which are all estimates

During the same period this year, there were about 12,000.

But that’s still higher than they were in 2009 before the surge, when nearly 8,000 insurgent attacks occurred. It was that number that convinced the White House and the Pentagon that more troops were needed.

The security force statistics, however, don’t account for attacks on Afghan troops unaccompanied by NATO forces. Afghan forces operating without NATO support is another trend the Pentagon frequently cites as a primary accomplishment this year.

The numbers also don’t reflect insurgent attacks on civilians, which the international security force notes is common. And it only counts a quarter of the “green-on-blue” attacks, where uniformed Afghans turn their guns on international forces serving alongside them, like last week’s checkpoint shooting.

As in Iraq, success in Afghanistan is dependent not just on battlefield victories, but on a counterinsurgency strategy, or to borrow an expression from Vietnam, another long and unpopular war, winning the “hearts and minds” of the people.

“Victory in Afghanistan won’t come with a shipboard surrender ceremony,” but when the Afghan people take control of their own destiny, said Pentagon spokesman George Little.

That means doing things like building roads and schools, and making everyday life safe.

Still, a former U.S. ambassador to NATO, Kurt Volker, said, “This doesn’t work if the motivation is ideology, if you fight because God wants you to fight. It becomes an impossible numbers game.”

The obstacle of ideology is clear in the fight against al Qaida. Pentagon and intelligence officials estimate that al Qaida has about 100 followers in Afghanistan, but in reality, only about a quarter are active and on the ground.

The international security force numbers show that al Qaida 10 fighters were killed or captured during the first half of September, which would seem to be a serious blow. But the terror group has no shortage of volunteers, according to Bernard Finel, an associate professor of national security strategy at the National War College.

“There are more people wanting to join an organization such as al Qaida than the organization can accommodate,” he said. “Can you ever cut off the flow of potential fighters?”

Meanwhile, the pullout of most allied troops by 2014 looms over any discussion of the success of the 11-year war and the way forward.

“Afghans know that the U.S. is leaving,” Finel said. “They also know all of these other groups will remain.”

It’s a waiting game, for everyone.

Jacqueline L. Hazelton, a visiting professor at the University of Rochester, who studies state-building through counterinsurgency, said in an email that given the enemy’s access to inside military information, the murderous episode at Camp Bastion suggests that “support for the state is not increasing.”

That, and the questions surrounding the numbers behind the claims of military success, she said, tell “a dismal story.”